The field of the invention is magnetic resonance imaging (“MRI”) systems and methods. More particularly, the invention relates to reducing specific absorption rate (“SAR”) in a subject imaged with an MRI system.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mxy. A signal is emitted by the excited nuclei or “spins”, after the excitation signal B1 is terminated, and this signal may be received and processed to form an image.
When utilizing these “MR” signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct an image using one of many well known reconstruction techniques.
The measurement cycle used to acquire each MR signal is performed under the direction of a pulse sequence produced by a pulse sequencer. Clinically available MRI systems store a library of such pulse sequences that can be prescribed to meet the needs of many different clinical applications. Research MRI systems include a library of clinically-proven pulse sequences and they also enable the development of new pulse sequences.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space.” Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp”, a “Fourier”, a “rectilinear”, or a “Cartesian” scan. The spin-warp scan technique employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of MR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (“2DFT”), for example, spatial information is encoded in one direction by applying a phase encoding gradient, Gy, along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient, Gx, in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse, Gy, is incremented, ΔGy, in the sequence of measurement cycles, or “views” that are acquired during the scan to produce a set of k-space MR data from which an entire image can be reconstructed.
Most MRI scanners use a single-channel RF excitation coil to tip the spin magnetization away from its equilibrium state and initiate a measurement cycle. Usually, a radio frequency (“RF”) excitation pulse is used to excite either all of the spins inside the excitation coil (non-selective excitation), a single slice through the subject (slice-selective excitation), or within only a specific region, such as, a small cube (3-D spatially-selective excitation). In spatially-selective, spatially-tailored excitation, the RF pulse is played out in the presence of gradient waveforms that impart a time-varying gradient onto the main magnetic field of the MRI system, which is instrumental in the spatial and selective excitation process. In general, the gradient field may be viewed as causing the traversal of a curve in excitation k-space, a path that may proceed through all three dimensions of k-space (kx, ky, and kz), which under certain assumptions is essentially a 3-D Fourier domain. During this traversal of excitation k-space, the energy of the RF pulse being played in conjunction with the gradient waveforms may be viewed as depositing RF energy along this k-space excitation trajectory curve. The RF pulse thus produces an excitation that modulates (in phase, in amplitude, or both) as a function of position (kx, ky, and kz) in excitation k-space. The resulting excitation is often closely related to the inverse Fourier transform of this deposited energy.
For example, in a typical slice-selective RF pulse, a constant gradient field is applied in the z-direction while an RF pulse shaped like a sine cardinal (“sinc”) function is transmitted through the MRI system's single excitation coil. In this instance, the gradient field causes the RF pulse energy to be deposited along a single line (a “spoke”) in the kz-direction of excitation k-space, that is, a line through the k-space position (0,0,kz). This sinc-like deposition in kz excites only those magnetic spins within a thin slice of tissue due to the Fourier relationship between energy deposited in excitation k-space and the flip angle of the resulting magnetization. In short, the magnetization that results from this typical RF pulse is a constant degree of excitation within the slice and no excitation out of the slice.
Recent work has extended this slice-selective concept to all three spatial dimensions, in which not only a thin slice is excited, but a particular pattern within the slice itself is excited. These “spatially-tailored” excitations in 2D and 3D require lengthy application of the RF excitation and associated gradients. A recent method, termed “parallel transmission” (and sometimes referred to as “parallel excitation”), exploits variations among the different spatial profiles of a multi-element RF coil array. This permits sub-sampling of the gradient trajectory needed to achieve the spatially-tailored excitation and this method has been shown in many cases to dramatically speed up, or shorten, the corresponding RF pulse.
This “acceleration” of the spatially-tailored RF excitation process makes the pulse short enough in duration to be clinically useful. Accelerations of 4 to 6 fold have been achieved via an 8 channel transmit system as disclosed by K. Setsompop, et al., in “Parallel RF Transmission with Eight Channels at 3 Tesla,” Magnetic Resonance in Medicine; 2006, 56:1163-1171. This acceleration enables several important applications, including flexibly shaped excitation volumes and mitigation of RF field inhomogeneity at high field for slice or slab-selective pulses. A number of methods have been proposed for the design of the RF and gradient waveforms for parallel excitation, such as those disclosed, for example, by U. Katscher, et al., in “Transmit SENSE,” Magnetic Resonance in Medicine; 2003, 49:144-150; by Y. Zhu in “Parallel Excitation with an Array of Transmit Coils,” Magnetic Resonance in Medicine; 2004, 51:775-784; by M. Griswold, et al., in “Autocalibrated Accelerated Parallel Excitation (Transmit-GRAPPA),” Proceedings of the 13th Annual Meeting of ISMRM; 2005, 2435; and by W. Grissom, et al., in “Spatial Domain Method for the Design of RF Pulses in Multicoil Parallel Excitation,” Magnetic Resonance in Medicine; 2006, 56:620-629.
Successful implementations have been demonstrated on multi-channel hardware, including those described by P. Ullmann, et al., in “Experimental Analysis of Parallel Excitation Using Dedicated Coil Setups and Simultaneous RF Transmission on Multiple Channels,” Magnetic Resonance in Medicine; 2005, 54:994-1001; by D. Xu, et al., in “A Noniterative Method to Design Large-Tip-Angle Multidimensional Spatially-Selective Radio Frequency Pulses for Parallel Transmission,” Magnetic Resonance in Medicine; 2007, 58:326-334; and by P. Vernickel, et al., in “Eight-Channel Transmit/Receive Body MRI Coil at 3T,” Magnetic Resonance in Medicine; 2007, 58:381-389.
Spatially-tailored excitations using parallel transmission methods are designed to provide a prescribed excitation pattern at the Larmor frequency of a specific spin species. As such, the parallel transmission of RF excitation pulses in the presence of two-dimensional (2D) and three-dimensional (3D) gradient trajectories offers a flexible means for volume excitation and the mitigation of main magnetic field, B0, and B1+ inhomogeneity. Parallel transmission systems are adept at these tasks because their RF excitation arrays include multiple independent transmission elements with unique spatial profiles that may be modulated and superimposed to tailor the magnitude and phase of the transverse magnetization across a chosen field-of-excitation (FOX). Parallel transmission systems are also promising because they enable one to reduce the duration of an RF pulse even after one has exhausted the ability to do so by increasing the amplitude and slew rates of the system's gradient coils. Namely, one may significantly undersample the excitation k-space trajectory (reducing the distance traveled in k-space), in turn shortening the corresponding RF pulse. The ability to “accelerate” in the k-space domain arises due to the extra degrees of freedom provided by the system's multiple transmit elements. Unfortunately, as described, for example, by U. Katscher and P. Bornert in “Parallel RF Transmission in MRI.” NMR Biomed, 19:393-400 (2006), using parallel transmission to accelerate a k-space trajectory increases peak pulse power, creating an additional specific absorption rate (“SAR”) concern beyond the aforementioned hot spot problem.
SAR, which is defined as the average energy deposition in an N-gram region over an extended period of time due to the application of one or more RF excitation pulses in units of watts per kilogram (“W/kg”), is a concern when conducting MRI experiments on human subjects, especially during the parallel transmission of spatially-tailored multi-dimensional excitation pulses through a multi-channel transmission system. This is because when multiple transmit channels are simultaneously employed, the local electric fields generated by each channel undergo local superposition and local extremes in electric field magnitude may arise, leading to spikes in local SAR that are of concern to regulatory bodies in both the United States and Europe. For a discussion of these regulatory concerns in the United States, see, for example, Center for Devices and Radiologic Health “Guidance for the Submission of Premarket Notifications for Magnetic Resonance Diagnostic Devices,” Rockville, Md.: Food and Drug Administration; 1998, and in Europe, see, for example, International Electrotechnical Commission, “International Standard, Medical Equipment-Part 2: Particular Requirements for the Safety of Magnetic Resonance Equipment for Medical Diagnosis, 2nd Revision,” Geneva: International Electrotechnical Commission; 2002. Recent studies have confirmed the consistent presence of “hot spots” and found that parallel transmitted pulses produce relatively-high ratios of local to whole-head average SAR, as is described by, for example, F. Seifert et al., in “Patient Safety Concept for Multichannel Transmit Coils,” J Magn Reson Imag, 26:1315-1321 (2007). These relatively-high ratios of local to whole-head average SAR make local SAR the limiting factor of parallel transmission MRI.
Recently, two methods have been proposed that attempt to address and mitigate parallel transmission SAR concerns by improving upon how parallel transmission pulses are designed. The first such method places l2 and l∞ constraints during the design of the RF waveform. Because the majority of pulse design methods generate a pulse by solving a linear system of equations, a simple way to indirectly reduce SAR is to impose regularizations while solving the linear system, constraining or reducing the root-mean-square or peak amperages of the resulting parallel transmission pulses. This approach requires no knowledge of the local electric field generated by each transmit array element, but it does not guarantee a SAR decrease because parallel transmission SAR does not scale directly as a function of the l2 and l∞ energies of a multi-channel RF pulse.
The second such SAR reduction method involves placing constraints on global and local SAR. In this method, SAR constraints are explicitly built into the pulse design process. Because both whole-head mean SAR and local N-gram SAR at any location may be expressed quadratically in terms of pulse sample values, constraints on both whole-head and local SAR may be incorporated simply by adding quadratic constraints to the design method. For example, the method described by I. Graesslin, et al., in “A Minimum SAR RF Pulse Design Approach for Parallel Tx with Local Hot Spot Suppression and Exact Fidelity Constraint,” Proc. Intl. Soc. Magn. Reson. Med., 2008; 612, explicitly accounts for global SAR as well as local SAR at several spatial locations by incorporating several quadratic constraints into the design. One limitation that seems unavoidable, however, is that in order to design truly SAR-optimal pulses, that is, ones where local SAR is guaranteed at all spatial locations in a given model, one is faced with the computationally-intractable problem of solving a system of equations with tens of thousands (millions) of quadratic constraints for moderate (high) resolution models.
The pulse design techniques discussed above focus on designing a single pulse with favorable SAR characteristics. This same pulse is then transmitted over many repetition time (“TR”) periods to accomplish the imaging task for which it is specifically designed. Thus, these SAR reduction methods are limited in that they spend all of their computation effort at designing only one parallel transmission RF pulse set that is then transmitted many times. Moreover, they assume that the best method for minimizing the maximum local SAR within a particular region of interest in a subject is to design one multi-channel pulse that has a minimum local SAR profile.
It would therefore be desirable to provide a computationally-efficient method for significantly reducing the local SAR within a localized spatial volume-of-interest in a subject using a plurality of different RF excitation pulses.